Least Common Multiple (LCM) of 31 and 45
The least common multiple (LCM) of 31 and 45 is 1395.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 31 and 45?
First, calculate the GCD of 31 and 45 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 31 ÷ 45 = 0 remainder 31 |
| 2 | 45 ÷ 31 = 1 remainder 14 |
| 3 | 31 ÷ 14 = 2 remainder 3 |
| 4 | 14 ÷ 3 = 4 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 10 and 69 | 690 |
| 12 and 174 | 348 |
| 173 and 153 | 26469 |
| 146 and 168 | 12264 |
| 22 and 151 | 3322 |